Sure, as I mentioned, the Gödel's incompleteness theorem proves that some things in mathematics can't be proven, here is a very simplistic video which explains it in 5 minutes
The paradox at the heart of mathematics: Gödel's Incompleteness Theorem.
Some things in physics can't also be experimented (at least not in the present moment) as I mentioned previously, because when you are dealing for example with such tiny things like electrons, the mere fact that you measure it alters drastically the result outcome, this is basically the uncertainty principle in a nut shell. So for instance, no one has ever seen an electron for this same reason but its presence has definitely been proven by JJ. Thompson, still, we know there is something called electron which produces some effects, but what exactly it is has not been proven, most people think of it as some kind of ball bearing, is that truly what it is? AFAIK nobody knows. Same thing happens in the large scale, when you talk about massive distances, etc... Even the Wilson/Penzias experiment which discovered cosmic background radiation supports the Big Bang theory but does not 100% prove it, how would you definitively prove the Big Bang? again, here consensus makes the decision.
Finally, future predictions, most are based on simulations or projections and the uncertainty is extremely high as to definitively prove such prediction, how would you definitely prove or disprove what such predictions claim?you can't do it beforehand, only in retrospective, if your prediction claims that in 30 years there won't be any drinking water left, you wait 30 years and determine if it was true or not, at which point it becomes a past prediction.